Methods and apparatus for accurate phase detection

ABSTRACT

A phase processor is disclosed which is configured to receive processed radar return data from a left radar channel, a right radar channel, and an ambiguous radar channel. The phase processor comprises a plurality of phase detectors each with an input and a reference input. The phase detectors are configured to determine a phase difference between radar return data received at the input and radar return data received at the reference input.

BACKGROUND OF THE INVENTION

This invention relates generally to radar systems, and more specificallyto a radar system which is capable of synchronization with a digitalelevation map (DEM) to accurately determine a location.

The proper navigation of an aircraft in all phases of its flight isbased to a large extent upon the ability to determine the terrain andposition over which the aircraft is passing. In this regard,instrumentation, such as radar systems, and altimeters in combinationwith the use of accurate electronic terrain maps, which provide theheight of objects on a map, aid in the flight path of the aircraft.Electronic terrain maps are well known and are presently used to assistin the navigation of aircraft.

Pulse radar altimeters demonstrate superior altitude accuracy due totheir inherent leading edge return signal tracking capability. The pulseradar altimeter transmits a pulse of radio frequency (RF) energy, and areturn echo is received and tracked using a tracking system. Theinterval of time between signal bursts of a radar system is called thepulse repetition interval (PRI). The frequency of bursts is called thepulse repetition frequency (PRF) and is the reciprocal of PRI.

FIG. 1 shows an aircraft 2 with the Doppler effect illustrated byisodops as a result of selection by the use of Doppler filters. The areabetween the isodops of the Doppler configuration will be referred to asswaths. The Doppler filter, and resulting isodops are well known in thisarea of technology and will not be explained in any further detail.Further, the aircraft 2 in the specification will be assumed to have avertical velocity of zero. As is known, if a vertical velocity exists,the median 8 of the Doppler effect will shift depending on the verticalvelocity. If the aircraft 2 has a vertical velocity in a downwarddirection, the median of the Doppler would shift to the right of thefigure. If the aircraft 2 has a vertical velocity in an upwarddirection, the Doppler would shift to the left of the figure. Again, itwill be assumed in the entirety of the specification that the verticalvelocity is zero for the ease of description. However, it is known thata vertical velocity almost always exists.

Radar illuminates a ground patch bounded by the antenna beam 10 from anaircraft 2. FIG. 1 a shows a top view of the beam 10 along with theDoppler effect and FIG. 1b shows the transmission of the beam 10 from aside view. To scan a particular area, range gates are used to furtherpartition the swath created by the Doppler filter. To scan a certainDoppler swath, many radar range gates operate in parallel. With therange to each partitioned area determined, a record is generatedrepresenting the contour of the terrain below the flight path. Theelectronic maps are used with the contour recording to determine theaircraft's position on the electronic map. This system is extremelycomplex with all the components involved as well as the number ofmultiple range gates that are required to cover a terrain area. As aresult, the computations required for this system are very extensive.

In addition to the complexity, the precision and accuracy of thedistance to a particular ground area or object has never been attainedusing an airborne radar processor.

BRIEF SUMMARY OF THE INVENTION

In one aspect, a phase processor configured to receive processed radarreturn data from a left radar channel, a right radar channel, and anambiguous radar channel is provided. The phase processor comprises aplurality of phase detectors each comprising an input and a referenceinput. The phase detectors are each configured to determine a phasedifference between radar return data received at said input and radarreturn data received at said reference input.

In another aspect, a method for processing radar return data isprovided. The radar return data includes radar return data received ateach of a right radar channel, a left radar channel, and an ambiguousradar channel. The method comprises receiving the radar return data at aphase processor and determining phase differences between the left,right, and ambiguous radar channels.

In still another aspect, a radar signal processing circuit is provided.The processing circuit comprises a radar gate correlation circuitconfigured to sample radar return data from left, right, and ambiguousradar channels at a sampling rate, a correlation bass pass filterconfigured to stretch the sampled radar return data to a continuous wave(CW) signal, and a mixer configured to down sample an in-phase componentand a quadrature component of the CW signal to a doppler frequency.Also, the processing circuit comprises a band pass filter centered onthe doppler frequency and a phase processor configured to receiveprocessed radar return data from the band pass filter. The phaseprocessor comprises a plurality of phase detectors each comprising aninput and a reference input, each phase detector configured to determinea phase difference between radar return data received at the input andradar return data received at the reference input.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1a is a diagram illustrating swaths made by a radar.

FIG. 1b is a diagram illustrating a radar transmit pattern.

FIG. 2 is an illustration of radar signal waveforms over time.

FIG. 3, is a diagram illustrating radar signals being received by threeantennas.

FIG. 4 is a diagram illustrating a body coordinate system.

FIG. 5 is a diagram illustrating a doppler coordinate system withrespect to the body coordinate system of FIG. 4.

FIG. 6 is a block diagram of a radar signal processing system.

FIG. 7 is a block diagram of a digital sampling and filtering section.

FIG. 8 is a block diagram of a correlation band pass filter.

FIG. 9 is a block diagram of a in-phase/quadrature mixer.

FIG. 10 is a block diagram of an all pass filter network for in-phaseand quadrature components of a signal, within the mixer of FIG. 8.

FIG. 11 is a diagram of a second order all pass filter.

FIG. 12 is a block diagram of a swath band pass filter.

FIG. 13 is a block diagram of a filter coefficients processor.

FIG. 14 is a velocity vector diagram.

FIG. 15 is a block diagram of a phase processor including three phasedetectors.

FIG. 16 is a block diagram of one phase detector from FIG. 15.

FIG. 17 is a block diagram of an interferometric angle resolver.

FIG. 18 is a chart illustrating varying electrical phase differencesbetween three antenna pairings.

FIG. 19 is a block diagram which illustrates inputs to a body coordinateprocessor.

FIG. 20 is a block diagram of the body coordinate processor of FIG. 19.

FIG. 21 is an illustration of the derivation of a doppler circle.

FIG. 22 is an illustration of the derivation of an interferometriccircle.

FIG. 23 is a diagram illustrating barker coded transmit and receivepulses.

FIG. 24 is a block diagram illustrating inputs to and outputs from arange verification processor

FIG. 25 is a flowchart illustrating a range verification method.

DETAILED DESCRIPTION OF THE INVENTION

There is herein described a combination Doppler radar/interferometer tonavigate an aircraft 2 with respect to terrain features below aircraft2. As used herein, aircraft is used to identify all flight platformswhich may incorporate a radar system, including, but not limited to,jets, airplanes, unmanned aerial vehicles, missiles, and guided weapons.The radar also functions with an electronic map, sometimes referred toherein as a digital elevation map (DEM), in determining a position ofaircraft 2. In addition to determining an altitude of aircraft 2, an XYZlocation of the nearest object to aircraft 2 on the ground, with respectto aircraft 2 in a certain terrain area can be determined. As aircraft 2is flying over terrain as shown in FIGS. 1a and 1 b, it is important todetermine a position of aircraft 2 in accordance with a map. A Dopplerfilter and range gate are used with a transmitted beam 10 from atransmit antenna.

In a general altitude range tracking radar, range is measured andindicated by measuring the time for transmitted energy to be reflectedfrom the surface and returned. With reference to FIG. 2, a radartransmitter repeatedly sends out bursts of electromagnetic energy at apredetermined repetition rate from an antenna, as indicated by transmitpulse 20. Following a time delay which is a function of the aircraftaltitude, a ground return pulse 22 is received by a receiving antennafeeding a receiver. A range gate 30 is utilized by the tracking radar toview at least a portion of ground return 22.

Referring to FIG. 3, three receive antennas, antenna R (right) 42,Antenna L (left) 44, and an ambiguous antenna (Ant Amb) 46, are used toreceive information. Along with the three antennas, three processingchannels, referred to below as left, right and ambiguous respectively,each include a receiver, a data acquisition device, range gate, and afilter. Use of the three antenna system, along with the processingdescribed herein, provides a solution to ambiguous detected angle of thenearest object. The ambiguous detected angle is due to the spacing ofthe antennas being greater than the transmitted RF frequency wavelength.By receiving three returns, the processing system is able to determinean umambiguous location of the nearest object on the ground, which inturn is utilized to locate position of aircraft 2 in body coordinates.Body coordinates are typically preferable than positioning as determinedby known systems, as those systems determine position as if the bodyaircraft 2 is aligned with the line of flight. As aircraft 2 is prone topitch, roll, and yaw, the body of aircraft 2 is not necessarily alignedwith the line of flight.

In an exemplary illustration, antenna R 42, along with processingsystems (described below) will provide a course range search whichroughly determines the range to the nearest point 48 in swath 12 (shownin FIG. 1) before aircraft 2 has passed over from swath 14 into swath12. Determination of the nearest point 48 is performed by a widebandwidth, high speed track loop which quickly determines the range tonearest point 48 in swath area 12. Nearest point 48 provides a startingpoint for a tracking loop using antenna L 44 and ambiguous antenna 46.The track loop controls the range gate to track returns from a transmitantenna. A narrow bandwidth, high precision processor is used to setrange gates for antenna L 44 and ambiguous antenna 46 to an exact rangeof nearest point 48 based on the previous course range determination.The operation of the three receive antennas and associated processingchannels provides a quick and accurate setting of a range gate on thenearest object in the Doppler swath 14 directly below aircraft 2 so thata phase difference can be measured and along with the known separations50 amongst the three antennas, a crosstrack distance to the object 48 isdetermined. The crosstrack distance is the distance, horizontal andperpendicular to the body coordinates of aircraft 2, to object 48.

FIG. 3 shows a view with aircraft 2 going into the Figure. During thephase comparison portion of the time interval, the Doppler filters ofthe left, right and ambiguous channels are set to select a swath 14(shown in FIG. 1) below aircraft 2. Further, both range gates are set ata range directly on the nearest object 48 as previously determined. Fromthis range, antenna R 42 receives a signal from object 48 at a distanceof R1, ambiguous antenna 46 receives a signal from the object 48 at adistance of RA, and antenna L 44 receives the signal from object 48 at adistance of R2 where the distance difference is a function of theantenna separation 50 between and amongst the three antennas. A phaseprocessor (described below) compares the phase difference between R1 andRA, R2 and RA, and R1 and R2 once the return signals are received. Asillustrated in the Figure, the exact range differences (R2−R1), (RA−R1),and (R2−RA) are from phase differences and simple trigonometry relationsare used to determine the exact crosstrack distance to the object 48 inaircraft body coordinates.

As illustrated in FIG. 3, after the range differences (R2−R1), (RA−R1),and (R2−RA) are determined and knowing the antenna separations 50, andmeasured range R1, then the crosstrack distance (Y) and verticaldistance (Z) can also 115 be computed in aircraft body coordinates. Itis important that the precise location of nearest object 48 in eachswath is determined so correlation can be made with the electronic mapswhich will accurately locate the aircraft 2 on the electronic map. Forexample, at typical high speed aircraft cruising velocities, a radar,configured with reasonably sized Doppler filters, has swath widths ofapproximately 10 feet at 5000 feet altitude. The resulting incidenceangle formed by the intersection of R1 and a vertical line 27 will thenbe on the order of less than 3 degrees. Basic trigonometry relationsshow that even with a typical error (for example 1%) on the radar rangegate measured distance R1, (50 feet at 5000 feet altitude), knowing theprecise antenna separation 50, and precise range differences (R2−R1),(RA−R1), and (R2−RA), the crosstrack distance (Y) will be precise due tothe very small incidence angle encountered.

FIG. 4 illustrates a body coordinate system. The body coordinate system,is the coordinate system with respect to aircraft body 2. An x-axis, Xmis an axis which passes through a nose of aircraft body 2. A y-axis, Ym,is an axis which is 90 degrees from Xm and is positive to the right ofaircraft body 2. A z-axis, Zm, is an axis which is 90 degrees from bothXm and Ym and perpendicular to a bottom of aircraft body 2. With respectto aircraft maneuvering, a positive roll is a drop of the right wing, apositive pitch is a nose up, and a positive yaw is the nose to theright, all with respect to a line of flight.

It is known that aircraft do not typically fly in alignment with theaircraft body coordinates. Such a flight path is sometimes referred toas a line of flight. Therefore an aircraft which is flying with one ormore of a pitch, roll, or yaw, and which has a hard mounted radarsystem, introduces an error element in a determination of targetlocation, in body coordinates. As such radars typically operate withrespect to the line of flight, a coordinate system with respect to theline of flight has been developed and is sometimes referred to as adoppler coordinate system. FIG. 5 illustrates differences betweenaircraft coordinates and doppler coordinates. An x-axis of the dopplercoordinate system, Xd, is on the line of flight. A y-axis, Yd, and az-axis, Zd, at right angles to Xd, respectively are defined as acrossXd, and above and below Xd.

Therefore, if aircraft 2 is flying with no pitch, roll, or yaw, the bodycoordinate system aligns with the doppler coordinate system. For apositive roll, Xm and Xd are still aligned, while Yd rotates below Ymand Zd rotates to the left of Zm. For a positive yaw, Xd rotates to theright of Xm, Yd rotates behind Ym, and Zd and Zm are aligned. For apositive pitch, Xd rotates above Xm, Yd aligns with Ym, and Zd rotatesahead of Zm. The complexity of having multiple of pitch, roll, and yaw,and determining a target position in aircraft body coordinates isapparent.

FIG. 6 is one embodiment of a doppler radar processing system 200.System 200 incorporates three radar antennas which receive reflectedradar pulses, the pulses having originated from a radar source. A leftantenna 202 receives the pulses and forwards the electrical signal toreceiver 204. Receiver 204 forwards the received radar signal to a dataacquisition unit 206. A right antenna 208 receives the pulses, at aslightly different time than left antenna 202, and forwards theelectrical signal to receiver 210. Receiver 210 forwards the receivedradar signal to a data acquisition unit 212. An ambiguity antenna 214also receives the reflected radar signal, and passes the received signalto a circulator 216. Circulator 216 functions to direct the transmitsignal to the antenna, and to direct the received signal from theantenna to receiver 220, thereby allowing a single antenna to be usedfor both transmitting and receiving. Receiver 220 forwards the receivedsignal to a data acquisition unit 222.

Data acquisition unit 206 provides a digital signal representative ofthe signal received at left antenna 202 to a left phase pre-processingunit 224. Similarly, representative signals are received atpre-processing units 226 and 228 from data acquisition units 222 and212, respectively. Data acquisition units 206, 212, and 222 areconfigured, in one embodiment, to sample received signals, and therebyreduce the data to a rate which allows a relatively low speed computerto process digitized radar data. In one embodiment, pre-processing units224, 226, and 228 perform a gate ranging function.

A phase processor 230 receives gated, filtered signals, representativeof left, right, and ambiguity signals received at the antennas, anddetermines a phase relationship between each of the left and ambiguoussignal, the right and ambiguous signals, and the right and left signals.The phase relationships between the signals are used, along with slantrange, velocity and attitude readings in a phase ambiguity processingunit 232 to determine an interferometric angle to a target. A bodycoordinate processor 233 utilizes the interferometric angle to determinean XYZ position of, for example, an aircraft employing system 200 withrespect to a current aircraft position, sometimes referred to herein asaircraft body coordinates.

A signal from data acquisition unit 222 is also received at an automaticgain control (AGC) unit 234. A signal from AGC unit 234 is passed topre-processing units 236, 238, and 240. A filtered signal frompre-processing unit 236 is passed to range track processor 242 whichprovides a slant range signal to phase ambiguity processing unit 232 andaltitude information. Pre-processing unit 238 passes a filtered signalto a range verification processor 244. Pre-processing unit 240 passes afiltered signal to a range level processor 246, which also provides afeedback signal to AGC 234.

FIG. 7 is a block diagram of a digital processing section 300 for system200 (shown in FIG. 6). Components in section 300, identical tocomponents of system 200, are identified in FIG. 7 using the samereference numerals as used in FIG. 6. Section 300 includespre-processing units 224, 226, 228, 236, 238, and 240 and processors230, 242, 244, and 246. Referring specifically to pre-processing units224, 226, 228, 236, 238, and 240, each includes a gate correlator 302, acorrelation band pass filter 304, a baseband I/Q mixer 306, and a swathband pass filter 308. A filter coefficients processor 309, in oneembodiment, is configured to provide at least a filter center frequencyin hertz, Fc, a filter bandwidth in hertz, B, and a filter samplingfrequency in hertz, Fs, to swath band pass filter 308, which uses Fc, B,and Fs in determination of filter coefficients. In one embodiment,processor 309 receives as input, an antenna mounting angle, velocityvectors in body coordinates, a pitch, and a slant range.

FIG. 8 is a block diagram of a correlation band pass filter 304 (alsoshown in FIG. 7). An input signal 310, sometimes referred to as x(0), isfed into a summing element 312. An output of summing element 312 ismultiplied by a coefficient 313, which, in one embodiment has a value of1/K1 (further described below). After multiplication by coefficient 313,an output signal 314, sometimes referred to as y(0), is generated.Another input into summing element 312 is provided by input signal 310being delayed by a two sample delay element 316, whose output, sometimesreferred to as x(−2), is fed into summing element 312. Further, outputsignal 314 is fed back into a second two sample delay element 318, whoseoutput, sometimes referred to as y(−2), is multiplied by a secondcoefficient 319, and fed into summing element 312. In one embodiment,coefficient 319 has a value of K3. Therefore, a present output, y(0) iscalculated as y(0)=(1K1)×[x(0)−x(−2)]−(K2×y(−2)), where K1=C+1, K3=C−1,K2=K3/K1, and C=1/Tan(π×bandwidth/f_(sample)) where bandwidth and samplefrequency are in hertz, and the angle for which the tangent is to becalculated is in radians.

In alternative embodiments, filter 304 is configured to filter rangeambiguity spectrum lines, filter out-of-band interference signals andstretch the input signal, which is a pulse, to a continuous wave (CW)signal. Filter 304, in one embodiment, receives as input an output ofgate/correlator 302 (shown in FIG. 7) at a sample rate of 100 MHz, an IFfrequency of 25 MHz, and has a bandwidth of 10 KHz. Therefore, in thisembodiment, there are four samples per IF frequency period.

A sample clock at 100 MHz provides samples at a 10 nsec rate. Forexample, a 4 μsec pulse repetition interval (PRI) (N=400 clocks per PRI)and two sample gate width, results in two non-zero gated return samples,x(0) and x(1), and 398 zero amplitude samples, x(2)−x(399), intocorrelation filter 304 during one PRI. In order to provide a filter ofreasonable processing size and speed, the zero amplitude samples whichdo not affect filter output are not processed by filter 304. Therefore,past outputs, for example y(−2), required in the filter feedbackconfiguration, as illustrated by delay elements 316 and 318, at the timeof non-zero inputs are not available. These past outputs are calculatedbased on filter outputs generated during and directly after the previousreturn (the previous non-zero samples), and filter droop characteristicsover a known pulse repetition interval.

In addition, one of the past outputs, y(−1), is not used because it hasa feedback multiplier with a value of nearly zero in one embodiment offilter 304, because of the narrow 10 kHz bandwidth.

In one exemplary embodiment, where F_(samples)=100 MHz, centerfrequency=25 MHz, and Bandwidth=8 KHz, coefficients are calculated asK1=3979.873661, K3=3977.873661, and K2=0.9994974715. Let P=the number ofsamples in a PRI. Filter 304 starts calculating at the beginning of agate width and continues for two counts after the end of the gate width.After the gate width+2 counts the next step is to calculate y(−2) andy(−1) and wait for x(P) data, the beginning of the next gate width,where x(P) is equivalent to x(0). Table 1 illustrates a generalprocedure for operation of filter 304, for low altitude radar data,track and phase gate of two sample widths, and a PRI of 400 μsec. Thecalculation for filter output y(0) requires filter output y(−2). Theexample of Table 2 example illustrates calculation of y(−2) where N=400,if PRI 4 μsec.

TABLE 1 Correlation Filter Algorithm Example x(N) Count (N) Algorithm 0397 y(−3) = y(397) 0 398 y(−2) = y(398) 0 399 y(−1) = y(399) x(0) 0 y(0)= (1/K1)[x(0) − x(−2)] − [K2 × y(−2)] x(1) 1 y(1) = (1/K1)[x(1) − x(−1)]− [K2 × y(−1)] 0 2 y(2) = (1/K1)[x(2) − x(0)] − [K2 × y(0)] 0 3 y(3) =(1/K1)[x(3) − x(1)] − [K2 × y(1)] 0 4 y(4) = 0 − K2 × y(2) = −K2 × y(2)= (−K2)¹× y(2) 0 5 y(5) = 0 − K2 × y(3) = −K2 × y(3) = (−K2)¹× y(3) 0 6y(6) = 0 − K2 × y(4) = −K2 × y(4) = −K2[(−K2) × y(2)] = (−K2)²× y(2) 0 7y(7) = 0 − K2 × y(5) = −K2 × y(5) = −K2[(−K2) × y(3)] = (−K2)²× y(3) 0 8y(8) = 0 − K2 × y(6) = −K2 × y(6) = −K2[(−K2) × (−K2) × y(2)] = (−K2)³×y(2) 0 9 y(9) = 0 − K2 × y(7) = −K2 × y(7) = −K2[(−K2) × (−K2) × y(3)] =(−K2)³× y(3) 0 10 y(10) = 0 − K2 × y(8) = −K2 × y(8) = −K2[(−K2) × (−K2)× (−K2) × y(2)] = (−K2)⁴× y(2) 0 11 y(11) = 0 − K2 × y(9) = −K2 × y(9) =−K2[(−K2) × (−K2) × (−K2) × y(3)] = (−K2)⁴× y(3)

In one embodiment, y(399) becomes y(0) if a range gate is moved in aninbound direction. The resulting P becomes 399. If a range gate is movedin an outbound direction, y(1) becomes y(0), and the resulting P becomes401. Algorithms shown for determination of y(4) through y(11) are usedto formulate a general algorithm equation.

In addition to an example illustration of calculation of y(−2) with a Pof 400 and a gate width of two clock counts, Table 2 also illustrates ageneral algorithm equation for counts (N) greater than three, (i.e.y(N)=(−K2)^(M)×y(2), for N even and y(N+1=(−K2)^(M)×y(3), whereM=(N(even)/2)−1.

TABLE 2 General Algorithm Equation after N = 3 Ein Count (N) Algorithm 0396 y(−4) = (−K2)¹⁹⁷ × y(2) 0 397 y(−3) = (−K2)¹⁹⁷ × y(3) 0 398 y(−2) =(−K2)¹⁹⁸ × y(2) 0 399 y(−1) = (−K2)¹⁹⁸ × y(3) x(0) 0 y(0) = (1/K1)[x(0)− x(−2)] − [K2 × y(−2)] x(1) 1 y(1) = (1/K1)[x(1) − x(−1)] − [K2 ×y(−1)] 0 2 y(2) = (1/K1)[x(2) − x(0)] − [K2 × y(0)] 0 3 y(3) =(1/K1)[x(3) − x(1)] − [K2 × y(1)]

In the embodiment described, for y(0) through y(3), the filter algorithmis calculated because new x(N) and/or y(N) data are available. After they(3) algorithm calculation, y(398) and y(399) are calculated, and thefilter algorithm is configured to wait for x(400) data, where x(400) isequivalent to x(0). If a range tracking algorithm dictates that x(0) bex(399), that is, the range gate causes the PRI to be shortened, theny(397) and y(398) are calculated. If the range tracking algorithmdictates that x(0) be x(401), that is, the range gate causes the PRI tobe increased, then x(399) and x(400) are calculated. The signal phase ispreserved by using the correct x(0) and y(−2). The PRI is not limited to4 μsec and can have a wide range of values. The filter algorithm isconfigured to set the N counter to count to 400 on the next cycle unlessthe range tracking algorithm requires 399 or 401 counts. In general, afilter configured similarly to filter 304 is capable of removing up toabout 95% of the mathematical operations that are required in knownfilter processing schemes.

Another exemplary embodiment of filter 304, for high altitude operation,incorporates a Barker code. Table 3 illustrates an exemplary embodiment,with a chip width equal to four, a PRI of 4 μsec, and P=400. In theexemplary embodiment, a 13 bit Barker code is used, and inputs x(0) andx(1) are data, x(2) and x(3) are filled with zeros, x(4) and x(5) aredata, x(6) and x(7) are filled with zeros, and the pattern continuesuntil N is equal to 51. Generally, the algorithm for N greater than 51is given as y(N)=(−K2)^(M)×y(50), for N even, andy(N+1)=(−K2)^(M)×y(51), where M=(N(even)−50)/2)−1.

TABLE 3 Barker codes at high altitudes example x(N) Count (N) Algorithm0 397 y(−3) = y(397) 0 398 y(−2) = y(398) 0 399 y(−1) = y(399) x(0) 0y(0) = (1/K1)[x(0) − x(−2)] − [K2 × y(−2)] x(1) 1 y(1) = (1/K1)[x(1) −x(−1)] − [K2 × y(−1)] 0 2 y(2) = (1/K1)[x(2) − x(0)] − [K2 × y(0)] 0 3y(3) = (1/K1)[x(3) − x(1)] − [K2 × y(1)] x(4) 4 y(4) = (1/K1)[x(4) −x(2)] − [K2 × y(2)] x(5) 5 y(5) = (1/K1)[x(5) − x(3)] − [K2 × y(3)] . .. . . . . . . 0 396 y(−4) = y(396) = (−K2)¹⁷² × y(50) 0 397 y(−3) =y(397) = (−K2)¹⁷² × y(51) 0 398 y(−2) = y(398) = (−K2)¹⁷³ × y(50) 0 399y(−1) = y(399) = (−K2)¹⁷³ × y(51) x(0) 0 y(0) = (1/K1)[x(0) − x(−2)] −[K2 × y(−2)] x(1) 1 y(1) = (1/K1)[x(1) − x(−1)] − [K2 × y(−1)] 0 2 y(2)= (1/K1)[x(2) − x(0)] − [K2 × y(0)]

FIG. 9 is a block diagram of a baseband IQ mixer 306. Mixer 306 isconfigured to reject negative Doppler shifts on the IF (IntermediateFrequency) input signal, which are behind aircraft 2, while allowing apositive doppler shift signal, from ahead of aircraft 2 to pass through.The positive doppler shift signal is equally forward as the negativedoppler shift signal is behind. Referring specifically to mixer 306, anIF in-phase portion includes a mixer 322 configured to operate at afrequency which is 1/PRI, where PRI is a radar pulse repetitioninterval, which converts the in-phase IF signal to Baseband (Doppler)frequency. Also included in the in-phase portion are a low pass filter324, a decimator 326, and an all pass filter 328. Referring specificallyto mixer 306, an IF quadrature portion includes a delay element 330,which produces the IF quadrature signal, and a mixer 332 configured tooperate at a frequency which is 1/PRI, where PRI is a radar pulserepetition interval, which converts the quadrature IF signal to Baseband(Doppler) frequency. Also included in the quadrature portion are a lowpass filter 334, a decimator 336, and an all pass filter 338. All passfilters 328 and 338 are configured to produce Baseband (Doppler)quadrature signals, which are received at a difference element 340,where the output of the all-pass filter 338 is subtracted from theoutput of the all-pass filter 328. The resulting difference signalcontains the positive or forward-looking Baseband (Doppler) signal,which is received at swath bandpass filter 308.

In particular embodiments, a frequency of data received at mixer 306 is25 MHz, and is referred to as an IF (intermediate frequency) signal.Mixer 306 in one embodiment, is configured to convert the 25 MHz IFsignal to baseband (or Doppler) frequencies, and further configured toreject negative Doppler frequencies. In specific embodiments, mixers 322and 332 are configured with PRIs which allow decimation of the signalfrom correlation bandpass filter 304 to a 25 kHz sample rate.Specifically, in the embodiment shown, the allowed Plus include 200,400, 500, 800, and 1000.

For purposes of description, a current input to low pass filter 324 isgiven as x1(0). A current output of the low pass filter 324 is thengiven as y1(0)=(1/K1)[x1(0)+x1(−1)]−[K2×y1(−1)], where x1(−1) and y1(−1)are respectively the previous input and output of the low pass filter324. A current input to low pass filter 334 is given as x0(0). A currentoutput of the low pass filter 334 is then given asy0(0)=(1/K1)[x0(0)+x0(−1)]−[K2×y0(−1)], where x0(−1) and y0(−1) arerespectively the previous input and output of the low pass filter 334.K1 is 1+(1/tan(πfo/Fs2), and K2 is 1−(1/tan(πfo/Fs2), where fo isbandwidth and Fs2 is a sampling frequency of low pass filters 324 and334. In one embodiment, the sampling frequency of low pass filters 324and 334 is the received signal frequency, Fs1, of 100 MHz divided by thepulse repetition interval.

The signals output from low pass filters 324 and 334 are further downsampled at decimators 326 and 336. In one embodiment, decimators 326 and336 are configured to sample at a frequency which is the pulserepetition interval multiplied by a sampling frequency, Fs3, of all passfilters 328 and 338, divided by the received signal frequency, or(PRI×Fs3)/Fs1.

FIG. 10 is a block diagram 350 of Baseband (Doppler) in-phase all-passfilter 328 and Baseband (Doppler) quadrature all-pass filter 338. In oneembodiment, all-pass filter 328 and all-pass filter 338 include fourcascaded second-order infinite impulse response (IIR) filters,configured to generate Baseband (Doppler) quadrature signals. Referringspecifically to all-pass filter 328, it includes filter elements 352,354, 356, and 358, sometimes referred to herein as a, b, c, and drespectively. Referring to all-pass filter 338, it includes filterelements 362, 364, 366, and 368, sometimes referred to herein as e, f,g, and h respectively.

FIG. 11 is a block diagram of one embodiment of a filter element 380.Element 380 is a representation of all of filter elements 352, 354, 356,358, 362, 364, 366, and 368 (shown in FIG. 9). The following descriptionrefers specifically to element 380, consisting of delay elements 392,396, 400, 404, summing element 386, and gain elements 384, 394, 398,388, 402, 406. For the purposes of description the current input 382 isreferred to as x(0). The current output 390 is then given asy(0)=[(A0x*(0))+(A1*x(−1))+(A2*x(−2))−(B1*y(−1))−(B2*y(−2))]/b0, wherex(−1) and y(−1) are respectively the previous input and output of filterelement 380, and x(−2) and y(−2) are respectively the previous-previousinput and output of filter element 380. A0, A1, A2, B1, and B2 refer tothe gain block coefficients.

In one specific embodiment, the above equation is applicable for all offilter elements 352, 354, 356, 358, 362, 364, 366, and 368 (shown inFIG. 9). The following are the coefficients for each filter element, theelements 352, 354, 356, 358, 362, 364, 366, and 368 being represented bya, b, c, d, e, f, g, and h respectively, and BBfreq is the base bandsampling frequency, and T is 1/BBfreq. In one embodiment, floating pointprecision is used.

Element a

a=1.0/0.3225;

w0=57.956;

A2=(4.0/T)/T+(2.0×w0×a/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0/T)/T−(2.0×w0×a/T)+w0×w0;

B2=(4.0/T)/T−(2.0×w0×a/T)+w0×w0;

B1=(−8.0T)/T+2.0×w0×w0;

B0=(4.0T)/T+(2.0×w0×a/T)+w0×w0;

Element b

b=1.0/0.4071;

w0=1198.2;

A2=(4.0/T)/T+(2.0×w0×b/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0/T)/T−(2.0×w0×b/T)+w0×w0;

B2=(4.0/T)/T−(2.0×w0×b/T)+w0×w0;

B1=(−8.0/T)/T+2.0×w0×w0;

B0=(4.0/T)/T+(2.0×w0×b/T)+w0×w0;

Element c

c=1.0/0.4073;

w0=16974.0;

A2=(4.0/T)/T+(2.0×w0×c/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0/T)/T−(2.0×w0×c/T)+w0×w0;

B2=(4.0/T)/T−(2.0×w0×c/T)+w0×w0;

B1=(−8.0/T)/T+2.0×w0×w0;

B0=(4.0/T)/T+(2.0×w0×c/T)+w0×w0;

Element d

d=1.0/0.3908;

w0=259583.5;

A2=(4.0/T)/T+(2.0×w0×d/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0T)/T−(2.0×w0×d/T)+w0×w0;

B2=(4.0/T)/T−(2.0×w0×d/T)+w0×w0;

B1=(−8.0/T)/T+2.0×w0×w0;

B0=(4.0/T)/T+(2.0×w0×d/T)+w0×w0;

Element e

e=1.0/0.3908;

w0=152.05;

A2=(4.0/T)/T+(2.0×w0×e/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0T)/T−(2.0×w0×e/T)+w0×w0;

B2=(4.0/T)/T−(2.0×w0×e/T)+w0×w0;

B1=(−8.0/T)/T+2.0×w0×w0;

B0=(4.0T)/T+(2.0×w0×e/T)+w0×w0;

Element f

f=1.0/0.4073;

w0=2326.03;

A2=(4.0/T)/T+(2.0×w0×f/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0/T)/T−(2.0×w0×f/T)+w0×w0;

B2=(4.0/T)/T−(2.0×w0×f/T)+w0×w0;

B1=(−8.0/T)/T+2.0×w0×w0;

B0=(4.0/T)/T+(2.0×w0×f/T)+w0×w0;

Element g

g=1.0/0.4071;

w0=32949.65;

A2=(4.0/T)/T+(2.0×w0×g/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0/T)/T−(2.0×w0×g/T)+w0×w0;

B2=(4.0T)/T−(2.0×w0×g/T)+w0×w0;

B1=(−8.0/T)/T+2.0×w0×w0;

B0=(4.0/T)/T+(2.0×w0×g/T)+w0×w0;

Element h

h=1.0/0.3225;

w0=681178.9;

A2=(4.0/T)/T+(2.0×w0×h/T)+w0×w0;

A1=(−8.0/T)/T+2.0×w0×w0;

A0=(4.0/T)/T−(2.0×w0×h/T)+w0×w0;

B2=(4.0/T)/T−(2.0×w0×h/T)+w0×w0;

B1=(−8.0/T)/T+2.0×w0×w0;

B0=(4.0/T)/T+(2.0×w0×h/T)+w0×w0;

FIG. 12 is a block diagram of one embodiment of a swath band pass filter308. Filter 308 is a first order band pass filter which is centered onthe doppler frequency. Filter 308 receives as input a signal, En, outputfrom IQ mixer 306 (shown in FIG. 9). Further inputs include a filtercenter frequency in hertz, Fc, a filter bandwidth in hertz, B, and afilter sampling frequency in hertz, Fs, which are provided.

A filtered output signal, Eo, is determined according toEo=(A0/B0)×En−(A0/B0)×En×Z⁻²−(B1/B0)×Eo×Z⁻¹−(B2/B0)×Eo×Z⁻². Referringspecifically to filter 308, the input signal, En 422 is received andmultiplied by a coefficient 424, with a value of A0/B0, and then appliedto a summing element 426. The output of summing element 426 is filteroutput 428. Input 422 is also delayed two counts by a two sample delayelement 430 whose output is multiplied by coefficient 432, with a valueof −A0/B0, and then applied to summing element 432.

Output 428 is multiplied by a sample delay element 434, whose output ismultiplied by a coefficient 436, with a value of −B1/B0, and thenapplied to summing element 432. Output 428 is also multiplied by a twosample delay element 438, whose output is multiplied by a coefficient444, with a value of −B2/B0, and then applied to summing element 432.Coefficients for filter 308 are determined according to Wb=2πB, which isbandwidth in radians, Wu=2π×(Fc+B/2), which is an upper 3 db point offilter 308 in radians, and Wl=2π×(Fc−B/2), which is a lower 3 db pointof filter 308 in radians. The coefficient A0 is 2×Fs×Wb, B0 is(4×Fs²)+(2×Fs×Wb)+(Wl×Wu), B1 is (2×Wl×Wu)−(8×Fs²), andB2=(4×Fs²)−(2×Fs×Wb)+(Wl×Wu).

FIG. 13 is a block diagram of a filter coefficients processor 309 (alsoshown in FIG. 7) which, in one embodiment, is configured to provideinputs to swath band pass filters 308 (shown in FIGS. 7 and 12).Processor 309 is configured to provide center frequencies Fc, for rangeswaths and phase swaths, and filter bandwidths, B, in hertz, for trackand phase swaths and level and verify swaths. By controlling swathfilter center frequencies, processor 309 is able to keep the dopplerswath centered in the antenna beam. Also filter bandwidth is controlled.The filter bandwidth is directly related to a down track swath width onthe ground such that a charge time for filter 308, inversely butdirectly related to bandwidth, is equal to the time it takes aircraft 2to fly across the swath width. Therefore, filter bandwidth is matched tovelocity of aircraft 2, and requires minimal processing. By knowing theantenna mounting angle, and the pitch of the aircraft, an angle to theantenna beam center is known, as described below, and a center frequencyis calculated, generally, according to Fc=2×Velocity×sin (angle)/radarwavelength.

Referring specifically to processor 309, an antenna mounting angle andvelocity vectors in body coordinates are input to determine a dopplervelocity, Vr 460, at a range swath center frequency according toVr=Vv×Cos(90−r−a)=Vv×Sin(a+r), where Vv=(Vx²+Vz²)^(0.5), whereVx=velocity component on body×axis and Vz=velocity component on body zaxis, a=A Tan(Vz/Vx), and r is the antenna mounting angle. A range swathcenter frequency, Fr 462 is determined according to Fr=2×Vr/L, where Lis a wavelength, and in one specific embodiment, is 0.2291 feet. Avelocity component on body y axis, Vy, is not used to center swath inantenna beam as the component has a value of zero'since the antenna isfixed to a y axis of the body.

Processor 309 is also configured to determine a phase swath dopplervelocity, Vp 464, which is delayed behind the range swath by a timeequal to the range processing delay. Vp is calculated asVp=Vv×Cos(90−(r−p)−a)=Vv×Sin(a+r−p), where Vv=(Vx²+Vz²)^(0.5), whereVx=velocity component on body×axis and Vz=velocity component on body zaxis, a=A Tan(Vz/Vx), r is the antenna mounting angle, andp=(T×Vx/H)×(180/π) in degrees, where T=1/πB and is a delay through rangeswath filter, T×Vx is vehicle movement on body X axis, B is the swathbandwidth, and H is altitude in feet. Phase swath center frequency 466is calculated according to Fp=2×Vp/L, where L is a wavelength, and inone specific embodiment, is 0.2291 feet.

Processor 309 is configured to determine a track and phase swathbandwidth, B 468 according to B=Vx/(0.6(H)^(0.5)) in hertz, where H isaltitude in feet. A level and verify swath bandwidth 470 is calculatedas a ratio of level and verify bandwidths to track and phase bandwidths,K, multiplied by track and phase swath bandwidth 468. FIG. 14 is avector diagram 500 which illustrates the 1calculations above described.In one embodiment, if the radar is in a range search mode, search rangeinstead of altitude is used to calculate bandwidth.

Together, filters 308 and processor 309 automatically configure theradar doppler filter center frequency and bandwidth to achieve betterradar performance over varying terrain and varying aircraft altitude,roll, and pitch than known systems. The determined center frequencyoperates to maintain the radar swath at an approximate center of theantenna beam. The calculated bandwidth is a bandwidth that controls thetrack swath width on the ground, and is calculated such that the filtertime constant is equal to the time it takes the vehicle to move acorresponding swath width distance. The bandwidth corresponds to a timeover the target and provides information as to how long a second swathlags a first swath. Phase channel swaths are set behind in position toaccount for a processing time of range processor 242 (shown in FIG. 7).The calculations of center frequency and bandwidth provide a mechanismfor keeping a swath slightly in front of the aircraft such that apositive doppler shift is realized.

FIG. 15 is a block diagram of a phase processor 230 (also shown in FIGS.6 and 7). Phase processor 230 includes three phase detectors 510, 512,and 514. In one embodiment, phase detectors 510, 512, and 514 areconfigured with an input and a reference input, and further configuredto determine a phase difference between the input and the referenceinput. Phase processor 230 is configured to receive processed radarreturn data, from swath band pass filters 308 (shown in FIG. 7), asdescribed above, for all of a left channel, a right channel, and anambiguous channel. Determination of phase difference in return data forthe three channels allows for an accurate position determination for anobject from which radar data was returned.

In the embodiment shown, phase detector 510 is configured to receiveambiguous channel return data as input, with left channel return data asa reference, and further configured to determine and output a phasedifference between the left and ambiguous channels. Phase detector 512is configured to receive right channel return data as input, withambiguous channel return data as a reference, and further configured todetermine and output a phase difference between the ambiguous and rightchannels. Phase detector 514 is configured to receive right channelreturn data as input, with left channel return data as a reference, andfurther configured to determine and output a phase difference betweenthe left and right channels.

FIG. 16 is a block diagram of phase detector 510 (shown in FIG. 15).Phase detectors 512 and 514 are of the same configuration. Phasedetector 510 incorporates a plurality of in-phase all pass filters 328and quadrature all pass filters 338 (shown above in FIGS. 9 and 10).Specifically, an input is received at a first in-phase filter 520(AP1.1) and a first quadrature filter 522 (AP1.2). A reference input isreceived at a second in-phase filter 524 (AP2.1) and a second quadraturefilter 526 (AP2.2). A multiplier 532 is configured to multiply outputsfrom filters 520 and 526. Another multiplier 534 is configured tomultiply outputs from filters 522 and 524. A third multiplier 536 isconfigured to multiply outputs from filters 520 and 524. A fourthmultiplier 538 is configured to multiply outputs from filters 522 and526. An output of multiplier 534 is subtracted from an output ofmultiplier 532 with a subtraction element 540 which produces a Y output542. An output of multiplier 536 is added to an output of multiplier 538with an addition element 544 which produces an X output 546. Aprocessing element 548 is configured to determine an arctangent of Youtput 542 divided by X output 546, which is the phase difference, inradians, between the input and the reference input.

In mathematical form, Y output 542 is calculated asY=(AP1.1×AP2.2)−(AP1.2×AP2.1), X output 546 is calculated asX=(AP1.1×AP2.1)+(AP1.2×AP2.2), and the phase difference is A TAN(Y/X).

In one embodiment, in-phase filters 520 and 524 and quadrature filters522 and 526 include the four cascaded second order infinite impulseresponse (IIR) filters as described in FIG. 10. Further, in theembodiment, filters 520 and 524 are configured to include in-phasefilter elements 352, 354, 356, and 358, (shown in FIG. 10) and areconfigured with coefficients which correspond to elements a, b, c, and drespectively as described above. Referring to quadrature filters 522 and526, they are configured to include quadrature filter elements 362, 364,366, and 368, (shown in FIG. 10) and are configured with coefficientswhich correspond to elements e, f, g, and h respectively as describedabove.

Once phase differences between the right, left, and ambiguous channelshas been determined, as described above, the phase differences are used,in one embodiment, to determine and interferometric angle to the target.FIG. 17 is a block diagram of phase ambiguity processing unit 232 (alsoshown in FIG. 6). In one embodiment, phase ambiguity processing unit 232is configured to receive an electrical phase difference between theambiguous channel and the left radar channel from phase detector 510, anelectrical phase difference between the right channel and the ambiguousradar channel from phase detector 512, and an electrical phasedifference between the right channel and the left radar channel fromphase detector 514.

Phase ambiguity processing unit 232 includes a phase bias adjust unit570 which provides a phase shift value which compensates for phaseshifts which occur in the routing of the radar signals, from receipt atan antenna and through cabling and processing areas within aircraft 2.It is accepted that most phase shifting of signals occurs due to cablingfor the routing of signals. Phase bias adjust 570 compensates for theambiguous channel with respect to the left radar channel. Phase biasadjust 572 compensates for the right channel with respect to theambiguous radar channel. Phase bias adjust 574 compensates for the rightchannel with respect to the left radar channel.

The compensated phase difference signals arc received at a phaseambiguity resolver 576. In one embodiment, phase ambiguity resolver 576is implemented using software, and determines a physical(interferometric) angle to a target which originally reflected the radarsignals received. Phase ambiguity resolution is further described below.After resolution of phase ambiguous signals, the physical angle signalis filtered utilizing a low-pass filter 578, and an angular position ofthe target with respect to aircraft body coordinates (X,Y,Z) isdetermined from the physical angle to the target using body coordinatesprocessor 233 (further described below). The determined position, in oneembodiment, is 90 degrees minus a half angle of a cone whose axis is aY-axis of the body of aircraft 2. The target is on the cone surface,therefore providing the subtraction from 90 degrees above described.

TABLE 4 Phase Ambiguity Resolution Matrix θ_(LA) θ¹ = θ_(LA) θ¹ =(θ_(LA) − 360) θ¹ = (θ_(LA) + 360) Φ=sin⁻¹(θ¹/K1) Φ=sin⁻¹(θ¹/K1)Φ=sin⁻¹(θ¹/K1) θ_(AR) θ¹ = θ_(AR) θ¹ = (θ_(AR) − 720) θ¹ = (θ_(AR) −360) θ¹ = (θ_(AR) + 360) θ¹ = (θ_(AR) + 360) Φ=sin⁻¹(θ¹/K2)Φ=sin⁻¹(θ¹/K2) Φ=sin⁻¹(θ¹/K2) Φ=sin⁻¹(θ¹/K2) Φ=sin⁻¹(θ¹/K2) θ_(LR) θ¹ =θ_(LR) θ¹ = (θ_(LR) − 720) θ¹ = (θ_(LR) − 360) θ¹ = (θ_(LR) + 360) θ¹ =(θ_(LR) + 360) Φ=sin⁻¹(θ¹/K3) Φ=sin⁻¹(θ¹/K3) Φ=sin⁻¹(θ¹/K3)Φ=sin⁻¹(θ¹/K3) Φ=sin⁻¹(θ¹/K3) θ_(LR) θ¹ = (θ_(LR) − 1080) θ¹ = (θ_(LR) +1080) Φ=sin⁻¹(θ¹/K3) Φ=sin⁻¹(θ¹/K3)

Table 4 is a phase ambiguity resolution matrix which is utilized, in oneembodiment, to determine a physical angle to a target based uponelectrical phase differences. A calculated electrical angle phasedifference, θ, is equivalent to [(360×S)/λ]×sin(Φ) or K×sin(Φ), where Φis the physical angle of the target in aircraft coordinates, S is aseparation between the two antenna elements in feet, and λ is awavelength of the radar signal in feet. In one particular embodiment,separation between the left antenna and the ambiguous antenna is 0.2917feet (3.5 inches), separation between the ambiguous antenna and theright antenna is 0.7083 feet (8.5 inches), and the separation betweenthe left antenna and the right antenna is 1 foot (12 inches). In theembodiment, the wavelength of the radar is 0.2291 feet. Therefore, inthe embodiment, and referring to Table 4, K1 is (360×0.2917)/0.2291, orabout 458.4, K2 is (360×0.7083)/0.2291, or about 1113.25, and K2 is(360×1)/0.2291, or about 1571.64. Physical angles are then determinedaccording to Φ=sin⁻¹(θ/K).

As antenna separation, radar wavelength, and aircraft position may allaffect a timing of radar signals received at the various antennas, phasedifferences, which are determined as described above, will change atvarying rates. In the embodiment illustrated in Table 4, physical anglesare calculated for multiple electrical phase differences, and the truephysical angle is a solution which provides approximately the samephysical angle calculation, in each of the three rows (within a coupleof degrees). Using the first antenna pairing (left and ambiguous), andbased on antenna separation, three possible physical angles aredetermined from the electrical phase difference received from phasedetector 510. As the second antenna pairing (ambiguous and right) arefurther apart, five possible physical angles are determined. The lastantenna pairing (left and right) are the furthest apart, therefore sevenpossible physical angles are determined. As described above, one of thephysical angles from each group of physical angle calculations, will beroughly equivalent, thereby providing an unambiguous physical anglesolution. In such a system it is important to note that separation inantenna pairing cannot be a multiple of radar wavelength.

FIG. 18 is a chart 600 illustrating varying electrical phase differencesbetween three antenna pairings. Chart 600 helps to illustrate theprocess above described. As varying electrical phase differences betweenthe three antenna pairings are charted, a single mechanical (physical )angle can be determined from the varying electrical phase differenceplots for each antenna pairing. That is, for a physical angle, there isone solution which provides a phase difference for each radar channelgrouping which is approximately equivalent to the calculated phasedifferences for the channel groupings.

FIG. 19 is a block diagram which illustrates inputs to and outputs frombody coordinate processor 233 (also shown in FIG. 6). Processor receivesthe phase detector angle to the target from phase ambiguity resolver 576via low pass filter 578 (described above in FIG. 17). Processor 233further receives the doppler swath filter center frequency, and thefilter bandwidth, a range to the target in feet, and velocity in pitch,roll and azimuth. Utilizing the processing described below, processor233 is configured to determine a distance to the target in aircraft bodycoordinates. In one embodiment, the distance is determined in feet foraircraft body coordinates x, y, and z. Processor 233 further determinesa velocity with respect to aircraft body coordinates in×and z.

FIG. 20 is a detailed block diagram of body coordinate processor 233 ofFIG. 19. Target range, vehicle velocity in pitch, roll, and azimuth,plus the swath filter center frequency and bandwidth are input into adoppler circle equation processor 620, which is configured to determinedoppler circle equations. The circle is determined using the swathfilter center frequency equation Fc=[2×V×cos(β)]/L, where V is velocity,L is wavelength, and β is an angle with respect to a line of flight,which is determined through manipulation of the above equation.Therefore, β=cos⁻¹((Fc×L)/(2×V)). A radius of the doppler circle, Rd, iscalculated according to Rd=target range×sin (β). A distance of thedoppler circle, Xd, from the aircraft is determined according toXd=target range×cos (β). FIG. 21 is provided to illustrate the equationswith regard to the doppler circle as derived above.

An example calculation is used to further illustrate. Inputs to dopplercircle equation processor 620 include a range to target of 2000 feet, avelocity of 800 feet/second, a wavelength of 0.229 feet, and a dopplerswath filter center frequency of 1213 Hertz. The angle with respect tothe aircraft line of flight, β, is determined asb=cos⁻¹((1213×0.229)/(2×800))=80 degrees. The doppler circle radius, Rd,is 2000×sin(80)=1969 feet, and distance of the doppler circle, Xd, is2000×cos(80)=347 feet.

Again referring to FIG. 20, processor 233 further includes aninterferometric circle equation processor 622 which is configured todetermine interferometric circle equations in body coordinates.Processor 622 receives as input a target range and the interferometricangle (or phase detector angle), a, to the target as calculated by phaseambiguity resolver 576 (shown in FIG. 17). An interferometric circleradius, Ri, is calculated as Ri=target range×cos(a). A location of theinterferometric circle on a Ym axis is determined as Ym=targetrange×sin(a). Referring to the example above, and including aninterferometric angle input of 15 degrees, the radius of theinterferometric circle, Ri, is 2000×cos(15), or 1932 feet. The locationof the circle on the Ym axis, Ym is 2000×sin(15), or 518 feet. FIG. 22is provided to illustrate the equations with regard to theinterferometric circle as derived above.

Again referring to FIG. 20, a doppler to body coordinate transformationprocessor 624 within processor 233 uses the doppler circle equation, andpitch, roll, and yaw inputs to transform the doppler circle into bodycoordinates. Finally, at intersection processor 626 which is configuredto solve equations to determine an intersection of the interferometriccircle equation with the doppler circle equation that has beentransformed into body coordinates.

In one embodiment, transforming begins by a determination of a velocityvector in body coordinates, from navigation data, N, (in pitch, roll,and yaw) according to ${{{{\begin{matrix}V_{X}^{N} \\V_{Y}^{N} \\V_{Z}^{N}\end{matrix}}\quad {{{TRANSPOSE}\quad {MATRIX}}}} = {\begin{matrix}V_{X}^{BODY} \\V_{Y}^{BODY} \\V_{Z}^{BODY}\end{matrix}}},}\quad$

where the transpose matrix is given by ${\begin{matrix}{\cos \quad (\psi)\quad \cos \quad (\theta)} & {{- \sin}\quad (\psi)\quad \cos \quad (\theta)} & {\sin \quad (\theta)} \\{{{\cos \quad (\psi)\quad \sin \quad (\theta)\quad \sin \quad (\varphi)} - {\sin \quad (\psi)\quad \cos \quad (\varphi)}}\quad} & {{{- \sin}\quad (\psi)\quad \sin \quad (\theta)\quad \sin \quad (\varphi)} - {\cos \quad (\psi)\quad \cos \quad (\varphi)}} & {{- \cos}\quad (\theta)\quad \sin \quad (\varphi)} \\{{\cos \quad (\psi)\quad \sin \quad (\theta)\quad \sin \quad (\varphi)} + {\sin \quad (\psi)\quad \cos \quad (\varphi)}} & {{\cos \quad (\psi)\quad \sin \quad (\varphi)} - {\sin \quad (\psi)\quad \sin \quad (\theta)\quad \sin \quad (\varphi)}} & {{- \cos}\quad (\theta)\quad \cos \quad (\varphi)}\end{matrix}},{{and}\quad \psi \quad {is}\quad {azimuth}},{\theta \quad {is}\quad {pitch}\quad {and}\quad \varphi \quad {is}\quad {{roll}.}}$

Velocity unit vectors (direction cosines) are given in body coordinatesas a_(x)=V_(x)/(V_(x) ²+V_(y) ²+V_(z) ²)^(½), a_(y)=V_(y)/(V_(x) ²+V_(y)²+V_(z) ²)^(½), and a_(z)=(V_(z)/(V_(x) ²+V_(y) ²+V_(z) ²)^(½).

Intersection processor 626 is configured to determine body coordinateswhich are calculated as X₁=D×a_(x), Y₁=D×a_(y), Z₁=D×a_(z), where thevelocity vector D, is given as R×cos(β), and β=cos⁻¹(Fc×L/2×V). B is thedoppler cone angle, Fc is the swath filter center frequency, R is therange to the target, V is (V_(x) ²+V_(y) ²+V_(z) ²)^(½), and L is thewavelength of the radar.

A position of the target in body coordinates is also calculated byintersection processor 626 as y=R×sin(A), where A=measured phase anglein body coordinates. The coordinate z is calculated asz=(−b±(b²−4ac)^(½))/(2×a), where a=1+(Z₁/K₁)², b=(−4Z₁×KT/(2X₁)²), andc=(KT/2X₁)²−KA. KA is calculated as (R×cos(A))², KB is calculated as(R×sin(B))², KY=(y×Y₁)², and KT is calculated as KT=KA+KY−KB+X₁ ²+Z₁ ².The coordinate x is calculated according to x=(KA−z²)^(½).

While determining a position of a radar target with respect to, forexample, an aircraft body, as described in detail above is necessary, itis also necessary in certain application to determine a range to atarget. As is well known, in high altitude radar operations, it ispossible that multiple radar transmit pulses will be transmitted beforea return pulse is received. This is sometimes referred to as theambiguous radar range problem. FIG. 23 illustrates one solution to theproblem, the solution being to modulate radar transmit pulses 650 with aphase code. Implementation of the code, which involves a phase shiftingof individual pulses of radar transmit pulses 650, allows asynchronization of transmit pulses 650 with return pulses 652 which arereceived by a radar. Synchronization of the phase encoded radar pulseswith the returned pulses is sometimes referred to as correlation.

In one embodiment, correlation is accomplished by implementation of aencoded radar scheme, and by looking for deviations in the return pulsesfrom a reference, or starting altitude. FIG. 24 is a block diagramillustrating inputs to and outputs from range verification processor 244(also shown in FIGS. 6 and 7). In one embodiment, verification processor244 is configured to step through encoded return signals and determine amain lobe of the return signal to determine a range to, for example, atarget.

Verification processor 244 is configured to receive as inputs, adetected radar return, which has been gated and demodulated.Verification processor 244 also receives as input a present internalrange to the target, and a command from the radar search logic to be ineither of a search mode or an acquisition mode. Verification processor244 is configured with a variable mainlobe threshold factor (describedbelow) and a verification dwell time, which is the time processor 244 isallocated to determine if an amplitude of a return signal exceeds thethreshold factor. A verify status output is set true of the amplitude ofthe radar return exceeds the threshold value, thereby signifying thatthe transmit radar pulses and return radar pulses are correlated. If notcorrelated, the verify status output is false, and processor 244provides a corrected range position to range processor 242 (shown inFIG. 7).

FIG. 25 is a flowchart 670 illustrating one embodiment of anautocorrelation process performed by processor 244. Referring toflowchart 670, a verify gate is set 672 to an internal range, from oneof track or search. It is then determined whether a radar return isacquired 674 from within a verify gate, the gate attempting to align thechips of transmitted and received codes. If no target is acquired 674,then processor 244 is configured to return to reset the verify gate. Ifa target is acquired 674, then an amplitude of the return is determined676. In addition, the threshold factor is set to, for example, fourtimes the determined amplitude and a counter is set to zero. The verifygate is stepped 678 out one chip of the code, the counter isincremented, and a dwell time passes before an amplitude of a return isagain read. If the amplitude read is determined 680 not to be above thethreshold factor, the counter is checked 682. If the counter isdetermined to be less than one less than the number of chips within thebarker code, the verify gate is again stepped 678, and the steps arerepeated, until the threshold factor is exceeded or the counter is equalto one less than the number of chips within the code. In one exemplaryembodiment, a thirteen bit code is used, therefore the counter has amaximum value of twelve. In one embodiment barker codes are used forencoding the radar signals.

If the threshold factor is not exceeded, the original acquisition is anacquisition on the main lobe of the return, and the transmit and returncodes are aligned, and the internal range as determined by processor 244is correct, resulting in a verification status being set 684 to verify.

If the threshold factor is exceeded, then the transmit and return codeshave become aligned. If the internal range has been moved 686 more thantwo range gates, the process illustrated by flowchart 670 begins anew.If there is a less than two range gate movement 686, the search logic ofthe radar is set 688 to not verify, and is moved by the value of thecounter, in order to align the transmit and receive barker codes. Theprocess illustrated by flowchart 670 again begins. The continuousprocessing of encoded radar transmit and return signals by processor,provides a favorable solution to the known radar range ambiguity problemby constantly stepping through the codes to ensure receipt of anunambiguous radar range return.

In one embodiment, the above described verification processing for radarrange ambiguity is applied continuously during flight, not just duringinitial acquisition. In utilization of such a system, the verificationprocessing is applied in order to resolve range ambiguity duringacquisition, but the processing is continuously applied afteracquisition, throughout the flight. The continuous processing is done inorder to ensure that if the transmit and received pulses becomemisaligned (loose correlation) the misalignment will both detected andcorrected. Loss of correlation could occur due to, for example, a rangediscontinuity due to severe aircraft rolls or a sudden change in terrain(i.e. flying over a cliff).

The verification processing is further illustrated through an example.In one embodiment, a phase code is used to resolve radar rangeambiguities and particularly a 13 bit phase code provides 20×log(13) or22 dB of rejection to range sidelobes. However, if verificationprocessor 244 should, for some reason, line itself on an ambiguous sidelobe, even if the mainlobe is for example 22 dB higher in amplitude,verification processor 244 will stay aligned with the sidelobe as longas there is a greater than 22 dB sensitivity margin. As stated above,one such example is flying over a sharp and deep cliff where a maximumradar track rate is less than a rate at which the range changes over thecliff. However, in practice, and assuming an ambiguous range sidelobe islined up, a transition to a decreased sensitivity margin will normallyresult in a less than sufficient margin to track the ambiguous rangeside lobe. Examples include flying over poor reflectivity ground orencountering a severe aircraft roll. The result is verificationprocessor 244 realigning into a proper and unambiguous line up onto themain lobe. Thus an ambiguous radar range does, after some time, normallycorrect itself. However, and especially with auto pilot systems, severeand dangerous aircraft altitude corrections will result during the timeof this very undesirable ambiguous range condition.

The method illustrated in flowchart 670 resolves the above illustratedsituation by continuously searching for the main lobe, while trackingwhat is believed to be the correct position, or lobe. If during theambiguity processing, or verification background search, it isdetermined that an ambiguous range is being tracked, an immediatecorrection is made to get the radar onto the correct range (i.e. themain lobe). To detect if the radar is on an ambiguous range track, the20 Log N equation is utilized to continuously determine differencesbetween the main lobe, and undesired side lobes.

The above described methods and systems describe a digital signalprocessing solution to known radar target position and range ambiguityproblems. Use of digital signal processing techniques therefore enablesa radar system to perform faster and more accurate airborne processingthan known radar ambiguity solutions. While the invention has beendescribed in terms of various specific embodiments, those skilled in theart will recognize that the invention can be practiced with modificationwithin the spirit and scope of the claims.

What is claimed is:
 1. A phase processor comprising a plurality of phasedetectors, each said phase detector determining a phase differencebetween any two of left radar channel return data, right radar channelreturn data, and ambiguous radar channel return data.
 2. A phaseprocessor according to claim 1 wherein at least one of said phasedetectors is configured to receive ambiguous radar channel return dataand receive left radar channel return data, said detector determining aphase difference between the ambiguous radar channel return data and theleft radar channel return data.
 3. A phase processor according to claim1 wherein at least one of said phase detectors is configured to receiveright radar channel return data and receive ambiguous radar channelreturn data, said detector determining a phase difference between theright radar channel return data and the ambiguous radar channel returndata.
 4. A phase processor according to claim 1 wherein at least one ofsaid phase detectors is configured to receive right radar channel returndata and receive left radar channel return data, said detectordetermining a phase difference between the right radar channel returndata and the left radar channel return data.
 5. A phase processoraccording to claim 1 wherein said phase detector comprises: an input; areference input; a first in-phase all pass filter connected to saidinput; a first quadrature all pass filter connected to said input; asecond in-phase all pass filter connected to said reference input; and asecond quadrature all pass filter connected to said reference input. 6.A phase processor according to claim 5 further comprising: a firstmultiplier configured to multiply outputs from said first in-phase allpass filter and said second quadrature all pass filter; a secondmultiplier configured to multiply outputs from said second in-phase allpass filter and said first quadrature all pass filter; a thirdmultiplier configured to multiply outputs from said first in-phase allpass filter and said second in-phase all pass filter; and a fourthmultiplier configured to multiply outputs from said first quadrature allpass filter and said second quadrature all pass filter.
 7. A phaseprocessor according to claim 6 further comprising: a subtractionelement; and an addition element, said subtraction element configured tosubtract an output of said second multiplier from an output of saidfirst multiplier, said addition element configured to add an output ofsaid third multiplier to an output of said fourth multiplier.
 8. A phaseprocessor according to claim 7 further comprising a processing elementconfigured to determine an arctangent of an output of said subtractionelement divided by an output of said addition element, the arctangentbeing the phase difference, in radians, between radar return datareceived at said input and radar return data received at said referenceinput.
 9. A phase processor according to claim 5 wherein said firstin-phase all pass filter, said first quadrature all pass filter, saidsecond in-phase all pass filter, and said second quadrature all passfilter each comprise four cascaded second order infinite impulseresponse (IIR) filters.
 10. A phase processor according to claim 9wherein said second order IIR filters operate according tooutput=((A0×input)+(A1×P_in)+(A2×PP_in)−(B1×P_out)−(B2×PP_out))/B0,where P_in is an input from a previous sample, PP_in is an input fromtwo samples previous, P_out is an output from the previous sample,PP_out is an output from two samples previous, and A0, A1, A2, B0, B1,and B2 are coefficients.
 11. A phase processor according to claim 10wherein said first in-phase all pass filter and said second in-phase allpass filter comprise: a first IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×a/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×a/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×a/T)+w0×w0,B1=(−8.0/T)/T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×a/T)+w0×w0, wherea=1.0/0.3225, w0=57.956, and T=1.0/a base band sampling frequency; asecond IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×b/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×b/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×b/T)+w0×w0,B1=(−8.0/T)/T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×b/T)+w0×w0, whereb=1.0/0.4071, w0=1198.2, and T=1.0/a base band sampling frequency; athird IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×c/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×c/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×c/T)+w0×w0,B1=(−8.0/T)/T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×c/T)+w0×w0, wherec=1.0/0.4073, w0=16974.0, and T=1.0/a base band sampling frequency; anda fourth IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×d/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×d/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×d/T)+w0×w0,B1=(−8.0/T)/T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×d/T)+w0×w0, whered=1.0/0.3908, w0=259583.5, and T=1.0/a base band sampling frequency. 12.A phase processor according to claim 10 wherein said first quadratureall pass filter and said second quadrature all pass filter comprise: afirst IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×e/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×e/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×e/T)+w0×w0,B1=(−8.0/T)T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×e/T)+w0×w0, wheree=1.0/0.3908, w0=152.05, and T=1.0/a base band sampling frequency; asecond IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×f/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×f/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×f/T)+w0×w0,B1=(−8.0/T)/T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×f/T)+w0×w0, wheref=1.0/0.4073, w0=2326.03, and T=1.0/a base band sampling frequency; athird IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×g/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×g/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×g/T)+w0×w0,B1=(−8.0/T)/T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×g/T)+w0×w0, whereg=1.0/0.4071, w0=32949.65, and T=1.0/a base band sampling frequency; anda fourth IIR filter configured with coefficientsA2=(4.0/T)/T+(2.0×w0×h/T)+w0×w0, A1=(−8.0/T)/T+2.0×w0×w0,A0=(4.0/T)/T−(2.0×w0×h/T)+w0×w0, B2=(4.0/T)/T−(2.0×w0×h/T)+w0×w0,B1=(−8.0/T)/T+2.0×w0×w0, and B0=(4.0/T)/T+(2.0×w0×h/T)+w0×w0, whereh=1.0/0.3225, w0=681178.9, and T=1.0/a base band sampling frequency. 13.A method for processing radar return data, the radar return dataincluding radar return data received at each of a right radar channel, aleft radar channel, and an ambiguous radar channel, said methodcomprising: receiving the radar return data at a phase processor; anddetermining phase differences between the left, right, and ambiguousradar channels.
 14. A method according to claim 13 wherein determiningphase differences between the left, right, and ambiguous radar channelscomprises: determining a phase difference between the ambiguous radarchannel return data and the left radar channel return data; determininga phase difference between the right radar channel return data and theambiguous radar channel return data; and determining a phase differencebetween the right radar channel return data and the left radar channelreturn data.
 15. A method according to claim 14 wherein receiving theradar return data at a phase processor comprises: receiving ambiguousradar channel return data at an input of a first phase detector withinthe phase processor; receiving left radar channel return data at areference input of the first phase detector; receiving right radarchannel return data at an input of a second phase detector within thephase processor; receiving ambiguous radar channel return data at areference input of the second phase detector; receiving right radarchannel return data at an input of a third phase detector within thephase processor; and receiving left radar channel return data at areference input of the third phase detector.
 16. A method according toclaim 14 wherein the phase processor includes a plurality of phasedetectors, the phase detectors having an input connected to a firstin-phase all pass filter and to a first quadrature all pass filter, anda reference input connected to a second in-phase all pass filter and toa second quadrature all pass filter, wherein determining a phasedifference comprises: multiplying outputs from the first in-phase allpass filter and the second quadrature all pass filter with a firstmultiplier; multiplying outputs from the second in-phase all pass filterand the first quadrature all pass filter with a second multiplier;multiplying outputs from the first in-phase all pass filter and thesecond in-phase all pass filter with a third multiplier; multiplyingoutputs from the first quadrature all pass filter and the secondquadrature all pass filter with a fourth multiplier; subtracting anoutput of the second multiplier from an output of the first multiplier;adding an output of the third multiplier to an output of the fourthmultiplier; and determining an arctangent of the subtraction resultdivided by the addition result, the arctangent being the phasedifference, in radians, between radar return data received at the inputand radar return data received at the reference input.
 17. A, methodaccording to claim 16 wherein the in-phase all pass filters and thequadrature all pass filters comprise four cascaded second order infiniteimpulse response (IIR) filters.
 18. A radar signal processing circuitcomprising: a radar gate correlation circuit that samples radar returndata from left, right, and ambiguous radar channels at a sampling rate;a correlation bass pass filter that processes the sampled radar returndata to form a continuous wave (CW) signal; a mixer that down samples anin-phase component and a quadrature component of the CW signal to adoppler frequency; a band pass filter receiving the doppler frequencyand centered on the doppler frequency; and a phase processor thatreceives filtered radar return data from said band pass filter, saidphase processor comprising a plurality of phase detectors, each saidphase detector determining a phase difference between a respective twoof the left radar channel return data, the right radar channel returndata, and the ambiguous radar channel return data.
 19. A radar signalprocessing circuit according to claim 18 wherein: a first of said phasedetectors receives ambiguous radar channel return data and left radarchannel return data, said detector determining a phase differencebetween the ambiguous radar channel return data and the left radarchannel return data; a second of said phase detectors receives rightradar channel return data and ambiguous radar channel return data, saiddetector determining a phase difference between the right radar channelreturn data and the ambiguous radar channel return data; and a third ofsaid phase detectors receives right radar channel return data and leftradar channel return data, said detector determining a phase differencebetween the right radar channel return data and the left radar channelreturn data.
 20. A radar signal processing circuit according to claim 18wherein said phase detectors each comprise: an input; a reference input;a first in-phase all pass filter connected to said input; a firstquadrature all pass filter connected to said input; a second in-phaseall pass filter connected to said reference input; and a secondquadrature all pass filter connected to said reference input.
 21. Aradar signal processing circuit according to claim 20 wherein said phasedetectors comprise: a first multiplier configured to multiply outputsfrom said first in-phase all pass filter and said second quadrature allpass filter; a second multiplier configured to multiply outputs fromsaid second in-phase all pass filter and said first quadrature all passfilter; a third multiplier configured to multiply outputs from saidfirst in-phase all pass filter and said second in-phase all pass filter;and a fourth multiplier configured to multiply outputs from said firstquadrature all pass filter and said second quadrature all pass filter; asubtraction element configured to subtract an output of said secondmultiplier from an output of said first multiplier; an addition elementconfigured to add an output of said third multiplier to an output ofsaid fourth multiplier, and a processing element configured to determinean arctangent of an output of said subtraction element divided by anoutput of said addition element, the arctangent being the phasedifference, in radians, between radar return data received at said inputand radar return data received at said reference input.
 22. A radarsignal processing circuit according to claim 20 wherein said all passfilters comprise four cascaded second order infinite impulse response(IIR) filters.